Anomalous diffusion analysis of the lifting events in the event-chain Monte Carlo for the classical XY models

Abstract

We introduce a novel random walk model that emerges in the event-chain Monte Carlo (ECMC) of spin systems. In the ECMC, the lifting variable specifying the spin to be updated changes its value to one of its interacting neighbor spins. This movement can be regarded as a random walk in a random environment with a feedback. We investigate this random walk numerically in the case of the classical XY model in 1,2, and 3 dimensions to find that it is superdiffusive near the critical point of the underlying spin system. It is suggested that the performance improvement of the ECMC is related to this anomalous behavior.

arXiv comment7 pages, 5 figures. (v2) Presentation including plots reorganized. Discussion of exponents in the infinite system size limit added

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Cited by in corpus (7)

• Event-chain Monte Carlo: foundations, applications, and prospects
• Irreversible Markov chains in spin models: Topological excitations
• Event-chain Monte Carlo with factor fields
• Hard-disk dipoles and non-reversible Markov chains
• Large-scale dynamics of event-chain Monte Carlo
• Symmetry breaking at a topological phase transition
• Emergent electrostatics in planar XY spin models: the bridge connecting topological order with broken $U(1)$ symmetry